5 citations · 13 across the 7 of their papers we have counts for
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Explicit Shimura's conjecture for Sp4
Kirill Vankov
Shimura's conjectire (1963) concerns the rationality of the generating series for Hecke operators for the symplectic group of genus g. This conjecture wes proved by Andrianov for a…
Explicit formulas for Hecke operators and Rankin's lemma in higher genus
Alexei Panchishkin, Kirill Vankov
We develop explicit formulas for Hecke operators of higher genus in terms of spherical coordinates. Applications are given to summation of various generating series with coefficien…
Explicit Shimura's conjecture for Sp3 on a computer
Alexei Panchishkin, Kirill Vankov
We compute by a different method the generating series in Shimura's conjecture for Sp3, proved by Andrianov in 1967. We develop formulas for the Satake spherical maps for Sp_n and…
Explicit formula for the spherical image of the symplectic Hecke series of genus four
Kirill Vankov
We obtain an explicit formula for the spherical image of the polynomial fraction conjectured by Shimura in 1963 for generating Hecke series in particular case of genus 4. As in our…
On the numerator of the symplectic Hecke series of degree three
Alexei Panchishkin, Kirill Vankov
We find a different method to compute the generating series in Shimura's conjecture for Sp3, proved by Andrianov in 1967. Formulas for the Satake spherical map for Sp3 are used.